Correlation Analysis
Correlation measures the strength and direction of the relationship between two variables. Different correlation methods are appropriate for different types of data and relationships.
Correlation Method
Select the correlation method you want to use:
Pearson Correlation Coefficient (r)
Measures the linear relationship between two continuous variables. Assumes that both variables are normally distributed and the relationship is linear.
When to use: For continuous, normally distributed data with a linear relationship.
Spearman Rank Correlation Coefficient (ρ)
Measures the monotonic relationship between two variables. Based on the ranks of the data rather than the raw values.
When to use: For ordinal data or when the relationship is monotonic but not necessarily linear.
Kendall's Tau (τ)
Measures the strength of dependence between two variables based on the concordance of pairs. More robust to outliers than other methods.
When to use: For small sample sizes or when there are many tied ranks in the data.
Correlation Results
Correlation Coefficient
Strength of Relationship
Coefficient of Determination
Variance explained
Statistical Significance
Interpretation
Scatter Plot
Descriptive Statistics
| Statistic | X Variable | Y Variable |
|---|---|---|
| Sample Size (n) | ||
| Mean | ||
| Standard Deviation | ||
| Minimum | ||
| Maximum |
Correlation Examples in Industrial Engineering
Production Example
Analyze the relationship between machine runtime and product defects to determine if longer runs lead to more quality issues.
Runtime (hrs): 8, 10, 12, 14, 16, 18, 20
Defects (count): 5, 7, 10, 15, 18, 22, 25
Quality Control Example
Examine the correlation between operator experience and product quality to inform training programs.
Experience (months): 3, 6, 12, 18, 24, 36, 48
Error Rate (%): 8.2, 6.5, 5.1, 4.3, 3.8, 3.2, 2.9
Supply Chain Example
Investigate the relationship between order quantity and delivery time to optimize inventory management.
Order Size (units): 100, 250, 500, 750, 1000, 1500, 2000
Delivery Time (days): 3, 5, 7, 10, 12, 15, 18
Interpreting Correlation Coefficients
| Correlation Coefficient | Strength of Relationship |
|---|---|
| ±0.9 to ±1.0 | Very strong |
| ±0.7 to ±0.9 | Strong |
| ±0.5 to ±0.7 | Moderate |
| ±0.3 to ±0.5 | Weak |
| 0 to ±0.3 | Very weak or none |
Note: Correlation does not imply causation. A strong correlation between two variables does not mean that one causes the other.